The first dispensation was the Jewish dispensation, when God acknowledged Israel’s calling. This began with Moses and the deliverance of Israel out of Egypt. Its ending was sealed by the Jews crucifying Jesus Christ. The second dispensation is the Christian dispensation, when God recognizes the calling of the church. This new dispensation replaced the Jewish one, for God no longer acknowledged the calling of the Jews. It began on the day of Pentecost and continues to this present day. The final dispensation will be the future millennium, when God turns back to acknowledging the unfilled calling of Israel. It will soon begin after the physical return of Jesus Christ in power and glory to this earth and world.
There is more biblical evidence which shows the validity of this three dispensation theology. Just as there were only two bible callings leading to three dispensations, in like manner there were only two religions which God gave to man, sanctioning their practice – Judaism and Christianity. The two sanctioned religions lead to seeing the same three dispensations. Also, in Scripture we only find two distinct transition periods between dispensations – again validating only three bible dispensations.
For more detail on the three dispensations: